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Question
Iron exhibits bcc structure at room temperature. Above 900°C, it transforms to fcc structure. The ratio of density of iron at room temperature to that at 900°C (assuming molar mass and atomic radii of iron remains constant with temperature) is ______.
Options
`(3 sqrt 3)/(4 sqrt 2)`
`(4 sqrt 3)/(3 sqrt 2)`
`sqrt 3/sqrt 2`
`1/2`
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Solution
Iron exhibits bcc structure at room temperature. Above 900°C, it transforms to fcc structure. The ratio of density of iron at room temperature to that at 900°C (assuming molar mass and atomic radii of iron remains constant with temperature) is `bbunderline((3 sqrt 3)/(4 sqrt 2))`.
Explanation:
In fcc atoms along face diagram touch each other, i.e., `sqrt 2 a = 4 r` ...(i)
In fcc atoms along body diagram touch each other, i.e., `sqrt 3 a = 4 r` ...(ii)
∴ a = `(4 r)/sqrt 2` ...[From (i)]
∴ a = `(4 r)/sqrt 3` ...[From (ii)]
∴ `d_"bcc"/d_"fcc" = ((Z_"bcc" xx M)/(N_A * a^3))/((Z_"fcc" xx M)/(N_A * a^3))`
= `(N_A((4 r)/sqrt 2)^3/(4 xx M))/(N_A((4 r)/sqrt 2)^3`
= `(3 sqrt 3)/(4 sqrt 2)`
